快速交替方向乘子法求解基于全变分的图像重建问题

采用一种快速的新型算法,即交替方向乘子法求解图像重建的全变分模型.首先,对全变分模型进行等价变形,使之转化成带有等式约束的可分的凸优化问题.然后,通过引入增广拉格朗日函数,并采用Gauss-Seidel迭代的思想,对问题中2块变量交替极小化,最后更新乘子.因为该方法充分利用了问题的特殊结构,将原问题分解成一系列容易求解...

Fast alternating direction method of multipliers for total-variation-based image restoration

A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.